Conservative agriculture practice adoption literature advocates that adoption is caused by many factors comprising cognitive, social, economic, personal, and CAP-related factors. Evaluating the adoption of CAPs as the outcome is complex and challenging with regression-based models as the systemic interdependencies of the factors offer diverse or varying results. Farmer production and environmental orientations as cognitive stances are notable interpreters of CAP adoption. The appetite level for risk-taking, innovativeness, and trust facilitates the adoption of CAPs. However, a causal-predictive technique should be (...) used to investigate the adoption of CAP. Hence, this study engages in a configuration approach using a fuzzy-set qualitative comparative analysis to analyze the patterns of different types of farmers' orientations, personal level of trust on extension services, and innovativeness risk-taking attitude on the intention to adopt CAPs. The analysis is based on the 155-farmer data collected employing a structured interview from Pakistan. The results suggest that a higher level of environment orientation and innovativeness is sufficient to increase the intention to adopt CAPs. Moreover, a higher intention to adopt CAPs is achieved with a lower production orientation, a higher personal level of innovativeness, and a risk-taking attitude of the farmer. The innovativeness can help to develop the intention to adopt the CAPs among the environment and production-oriented farmers. Causal solutions offer a unique understanding that the farmers' environment and production orientation can combine to suggest inclined to adopt CAPs by having an attitude of innovativeness and risk-taking. The causal solutions achieved significant predictive validity in the holdout samples. Policy and farmer-level suggestions were made to raise the intention to adopt CAPs among the farmers. (shrink)

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related (...) to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state. (shrink)

As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image of a complex subalgebra and a (...) complex left reduced ideal. (shrink)

This is the first part of a two-part paper in which I conclude the process, initiated elsewhere, of tracking objective conditions of vagueness of representation from language to pictures, from philosophy to imaging science, from vagueness to approximation, from representation to reasoning, with a focus on the application of fuzzy set theory and its challenges.

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The multiobjective optimization on the basis of ratio analysis method captures diverse features such as the criteria and alternatives of appraising a multiple criteria decision-making problem. At the same time, the multiple criteria problem includes a set of decision makers with diverse expertise and preferences. In fact, the literature lists numerous approaches to aid in this problematic task of choosing the best alternative. Nevertheless, in the MCDM field, there is a challenge regarding intangible information which is commonly involved in multiple (...) criteria decision-making problem; hence, it is substantial in order to advance beyond the research related to this field. Thus, the objective of this paper is to present a fused method between multiobjective optimization on the basis of ratio analysis and Pythagorean fuzzy sets for the choice of an alternative. Besides, multiobjective optimization on the basis of ratio analysis is utilized to choose the best alternatives. Finally, two decision-making problems are applied to illustrate the feasibility and practicality of the proposed method. (shrink)

It, is shown that Birkhoff –von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Łukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Łukasiewicz intersection and (...) union of fuzzy sets in the first case and Łukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Łukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered. (shrink)

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)-hesitant fuzzy ideal generated by a hesitant fuzzy ideal in (...) a semigroup. In addition, we also introduce the concepts of \((\alpha,\beta)\)-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)-hesitant fuzzy left ideals and \((\alpha,\beta)\)-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of \((\alpha,\beta)\)-hesitant ideals are given. (shrink)

As an introduction to our work, we emphasize the parallel interpretation of abstract tools and the concepts of undetermined and vague information. Imprecision, uncertainty and their relationships are inspected. Suitable interpretations of the fuzzy sets theory are applied to legal phenomena in an attempt to clearly circumscribe the possible applications of the theory. The fundamental notion of reference sets is examined in detail, hence highlighting their importance. A systematic and combinatorial classification of the relevant subsets of the legal field (...) is supplied for practical application. Although the use of the fuzzy sets theory is sometimes suggested as a palliative measure (no competition exists), it can also be complementary (serve as a building block to improve modelisation). An Appendix gives a brief recall of the key-concepts of the axiomatic theory of fuzziness and its developments: fuzzy sets, fuzzy logic, fuzzy control and theory of possibility. (shrink)

The relationship between vague statements and fuzzy sets is examined. It is shown that the probability of vague statements may be defined in a manner analogous to that discussed in Reichenbach's logic of weight.

This paper examines a novel notion of causality, namely, fuzzy-set-theoretic causality. Over the last decade, a number of conceptual models of causality, in the language of fuzzy-set theory, have appeared in the scientific literature and have been applied to empirical research. They have circulated widely from one scientific discipline to another, weaving a unifying thread through them. However, they have received no philosophical attention. In this paper, I will discuss the value and limitations of this type of model (...) and will read into its application several dimensions of philosophical significance. (shrink)

This paper is devoted to the study of the notion of the phase-space representation of quantum theory in both the nonrelativisitic and the relativisitic cases. Then, as a derived concept, the stochastic phase space is introduced and its connections with fuzzy set theory and probabilistic topological (in particular, metric) spaces are discussed.

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice L. (...) In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy n-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is n-c.e. if its membership function can be approximated by changing monotonicity at most n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy n-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} fuzzy sets. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and (...) class='Hi'>fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (shrink)

Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy predicate logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.

We have introduced for the first time the degree of dependence (and consequently the degree of independence) between the components of the fuzzy set, and also between the components of the neutrosophic set in our 2006 book’s fifth edition [1]. Now we extend it for the first time to the refined neutrosophic set considering the degree of dependence or independence of subcomponets.

We have introduced for the first time the degree of dependence (and consequently the degree of independence) between the components of the fuzzy set, and also between the components of the neutrosophic set in our 2006 book’s fifth edition [1]. Now we extend it for the first time to the refined neutrosophic set considering the degree of dependence or independence of subcomponets.

Based on the expanded theory of planned behavior, this study first explores the configuration relationship between founder management and innovation by using the fuzzy-set qualitative comparative analysis. Based on the theory of planned behavior, this study divides the behavior intention of founders into three categories: Attitude, subjective norm, and perceived behavior control. Using fsQCA, we found that there are two ways to achieve high innovation input of enterprises. In combination with the two ways, the factors such as male and (...) highly educated founder, and large firm size can effectively increase the innovation input of firms, which is consistent with the three aspects of the behavioral intention of the theory of planned behavior, and it proves that the theory of planned behavior can effectively explain the configuration relation between the founder and firm innovation. In addition, this study finds that the innovation output is different from the innovation input, is dependent on the innovation ability of the firm itself, and is less influenced by the external environment. (shrink)

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function (...) and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. (shrink)

PurposeDrawing upon the stimulus-organism-response model, this paper aims to investigate the effects of stores’ environmental components on Chinese consumers’ emotions and intentions to purchase luxury brands.Design/Methodology/ApproachData were collected from Chinese consumers who have purchased luxury brands from retail stores. Partial least squares-structural equation modeling and fuzzy-set qualitative comparative analysis were employed for data analysis.FindingsThe results of PLS-SEM indicated that three dimensions of the store environment directly and significantly influenced Chinese consumers’ emotions. However, fsQCA revealed greater heterogeneity among respondents by (...) highlighting stores’ environmental components and Chinese consumers’ emotions.Originality/ValueThis study makes significant contributions to the marketing literature by examining the S-O-R model alongside fsQCA approach to conditionally predict outcomes in a luxury brand context. The present study may be one of the first to examine the effects of stores’ environmental components on Chinese consumers’ emotions and purchase intentions, applying both symmetrical test and asymmetrical test approaches to determine significant components of the store environment as well as component combinations that predict Chinese consumers’ emotions and purchase intentions. (shrink)

The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem because it combines the advantages of the neutrosophic cubic set and the hesitant fuzzy set. The algebraic operations based on Dombi norms and co-norms are more flexible than the usual algebraic operations as they involve an operational parameter. First, this paper establishes Dombi algebraic operational laws, score functions, and similarity measures in neutrosophic cubic hesitant fuzzy sets. Then, we proposed Dombi exponential (...) operational laws in which the exponents are neutrosophic cubic hesitant fuzzy values and bases are positive real numbers. To use neutrosophic cubic hesitant fuzzy sets in decision-making, we are developing Dombi exponential aggregation operators in the current study. In the end, we present applications of exponential aggregation operators in multiattribute decision-making problems. (shrink)

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α, δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to (...) a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ. (shrink)

In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image (...) edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques. (shrink)

Many criticisms of prototype theory and/or fuzzy-set theory are based on the assumption that category representativeness (or typicality) is identical with fuzzy membership. These criticisms also assume that conceptual combination and logical rules (all in the Aristotelian sense) are the appropriate criteria for the adequacy of the above “fuzzy typicality”. The present paper discusses these assumptions following the line of their most explicit and most influential expression by Osheron and Smith (1981). Several arguments are made against the (...) above identification, the most important being that representativeness in prototype theory is exclusively based on element-to-element similarity while fuzzy membership is inherently an element-to-category relationship. Also the above criteria for adequacy are criticized from the viewpoint of both prototype theory and fuzzy-set theory as well as from that of both conceptual and logical combination, and also from that of integration. (shrink)

Green entrepreneurship has a huge role in solving environmental degradation and social problems. As today’s youth are tomorrow’s entrepreneurs, enhancing their green entrepreneurial intention will contribute to the sustainable development of economy in the future. The existing literature has examined the green entrepreneurial intention of college students based on self-efficacy, entrepreneurial creativity, entrepreneurship education, financial support, sustainable development values, and other influencing factors. However, these studies focus on net effect of factors on the results of college students’ green entrepreneurial intention, (...) ignoring the combination of multiple factors, and the relationship between different configurations of factors and the results of college students’ green entrepreneurial intention. Therefore, this study aimed to understand and analyze the influence of the complex relationship between multiple antecedents on college students’ green entrepreneurial intention from a comprehensive perspective. Based on 207 questionnaires collected from colleges in the coastal cities of China, this study used the fuzzy set qualitative comparative analysis method for data analysis. The results showed three dominant paths of great significance to college students’ high green entrepreneurial intention: entrepreneurial creativity—green cognition—dominant path; entrepreneurial creativity—financial support—dominant path; and the future self-continuity—entrepreneurship culture—entrepreneurship education—dominant path. The results of this study can help college educators to plan courses on innovative thinking and green entrepreneurship to improve college students’ entrepreneurial creativity and green cognitive ability. (shrink)

In this article codes over lattice valued intuitionistic fuzzy set type-3 are defined. Binary block codes and linear codes are constructed over LIFS-3. Hamming distance and related properties of these newly established codes are examined. The research findings are applied to genetic codes. The set L of sixty-four codons is converted into a lattice and then codes are created over the set S of twenty amino acids by defining membership and nonmembership functions from the set of twenty amino acids (...) to the sixty-four codon set. Comparison of codes over L -fuzzy set and LIFS-3 conducted in terms of hamming distance for codon system that ensures the efficiency of newly established codes. (shrink)

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by (...) experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy. (shrink)

Trapezoidal interval type-2 fuzzy sets are a special kind of type-2 fuzzy sets. TIT2FSs are useful in dealing with fuzziness inherent in decision data and the decision-making process. For multi-attribute group decision-making problems in which the attribute values and attribute weights are TIT2FSs, a new decision-making approach is proposed. On the basis of the concept of barycenters, a new approach to ranking TIT2FSs is given. Four kinds of geometric aggregation operators for TIT2FSs are developed, including the TIT2FS weighted (...) geometric average operator, TIT2FS ordered weighted geometric average operator, TIT2FS hybrid weighted geometric average operator, and extended TIT2FS hybrid weighted geometric average operator. The individual comprehensive values of alternatives are derived through the extended TIT2FS weighted geometric average operators. Using the TIT2FS hybrid weighted geometric average operator and the expert weights, the individual comprehensive values of alternatives are integrated into the collective ones, which are used to rank the alternatives. The practicability and effectiveness of the developed method are illustrated with a teaching quality assessment example. (shrink)

In this paper, we utilized triangular conorms. The essence of using S-norm is that the similarity order does not change using different norms. In fact, we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity (...) of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate this method. (shrink)

The purpose of the study is to investigate the features of the algorithm for forming the stock portfolio of investors using the theory of fuzzy sets, taking into account a priori uncertain input information and market dynamics. The scientific novelty of the article lies in the application of a relatively new fuzzy-multiple apparatus and the theory of fuzzy sets to the formation of the stock portfolio of investors. From a practical point of view, the proposed fuzzy (...) model makes it possible to predict not only the structure and expected return of a portfolio of securities, similarly to the application of the classical portfolio theory, but also to obtain the values of the lower and upper boundaries of the return on securities, which will allow the investor to form a more complete picture of the structure of the portfolio in the future. As a result, it was found that the use of classical statistical approaches for the formation of a stock portfolio of investors will not allow obtaining a reliable and accurate result, since traditional methods do not take into account the uncertainty factors of events in the stock market. To level information asymmetry and eliminate risks of uncertainty, it is advisable to apply the theory of fuzzy logic. (shrink)